Orthoptic curve (director circle) of an ellipse

The orthoptic curve of a plane curve C is the geometric locus of points through which passes a pair of perpendicular tangents to C. If C is an ellipse, then its orthoptic curve is a circle. Check the ellipse and its director circle when changing the parameters in the canonical equation of the ellipse (i.e. changing the eccentricity of the ellipse). The following paper elaborates on this topic and checks generalizations: Th. Dana-Picard, G. Mann and N. Zehavi (2011): From conic intersections

to toric intersections: the case of the isoptic curves of an ellipse, The Montana Mathematical Enthusiast 9 (1), 59-76.available: http://www.math.umt.edu/TMME/vol9no1and2/index.html.